Three-dimensional charged Einstein-aether black holes and the Smarr formula

Abstract

We investigate behaviors of the three-dimensional gravity coupled to a dynamical unit timelike vector, the aether, and present two new classes of exact charged solutions. When ${c}_{13}=0$, ${\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{'}}=0$, we find the solution is the usual BTZ black hole but now with a universal horizon. In the frame of black hole chemistry, we then calculate the temperature of the universal horizons and construct the Smarr formulas and first law in the three cases: (quasi)asymptotically flat, aether asymptotically flat, and quasi-BTZ black hole spacetime. We found these universal horizons obey an exact (or slightly modified) first law of black hole mechanics and may have an entropy, and the black hole mass can be interpreted as enthalpy of spacetime. Then the holography may be extended to these horizons under violating Lorentz symmetry.